Differentiation - true/false calculus quiz
The maximum slope of the graph of the graph of y=sin(bx) is b
.
A continuous function must have a minimum on an open interval
False
A function has at most one maximum on an interval
False
Every nth-degree polynomial has (n-1) critical numbers
False
If a function is continuous, then it is differentiable
False
If a<c<b and c is a critical number of ∫, then ∫ has a relative extrema in (a, b)
False
If c is a critical number of ∫, then ∫ has a relative extrema at x=c
False
If f''(c)=0, then the graph of ∫ has a point of inflection at (c, f(c))
False
If the graph of a function has three x-intercepts, then it must have at least two points at which its tangent line is horizontal
False
If the graph of a function possesses a tangent line at a point, then it is differentiable at that point
False
If y=(1-z)^½, then y'=½(1-x)^⁻½
False
If y=1/∫(x), then y'=1/∫'(x)
False
If y=π², then dy/dx=2π
False
If y=∫(x), ∫ is increasing and differentiable, and ∆x>0, then ∆y≥dy
False
If y=∫(x)g(x), then dy/dx=∫'(x)g'(x)
False
If y=∫(x)g(x), then y''=∫(x)g''(x)+g(x)f''(x)
False
If ∫ and g are differentiable, then the quotient ∫/g is differentiable
False
If ∫ is differentiable at x=c, then ∫' is differentiable at x=c
False
If ∫ is increasing and continuous on (a,b), then ∫ is differentiable on (a,b)
False
If ∫'(x) = g'(x), then ∫(x) = g(x)
False
If ∫(x) is an nth-degree polynomial, then f^(n)(x)=0
False
If ∫(x)=sin²(2x), the ∫'(x)=2(sin2x)(cos2x)
False
The Mean Value Theorem can be applied to ∫(x)=1/x on the interval [-1,1]
False
The average rate of change is always larger than the instantaneous rate of change
False
The equation of the line that is tangent to the graph of y=x² at the point (-1,1) is y-1=2x(x+1)
False
The function y=∫(x) can have at most one horizontal asymptote
False
The graph of ∫(x)=1/x is concave downward for x<0 and convince upward for x>0, and thus it has a point of inflection when x=0
False
The graphs ∫(x)=sinx and g(x)=cosx intersect at right angles
False
The maximum value of y=3sinx+2cosx is 5
False
The product of two increasing functions is increasing
False
The roots of √∫(x) = 0 coincide with the roots of f(x) = 0
False
The slope of the graph of y=x³ is different at every point on the curve
False
The tangent line to a curve at a point can touch the curve at only one point
False
The zeros of ∫(x)=p(x)/q(x) coincide with the zeros of p(x)
False
d/dx(√cx) = cd/dx(√x)
False
A continuous function must have a minimum on a closed function
True
An nth-degree polynomial has at most (n-1) critical numbers
True
Every second-degree polynomial possesses precisely one relative extrema
True
If (x+1)² is a factor of ∫(x), then (x+1) is a factor f'(x)
True
If 0<a<b<1 and ∫ is differentiable on (0,1), then ∫ is continuous on [a,b]
True
If a function is differentiable, then it is continuous
True
If the coefficients of a polynomial function are all positive, then the polynomial has no positive zeros
True
If the derivative of a function is zero at a point, then the tangent line at the point is horizontal
True
If the graph of a polynomial function has three x-intercepts, then it must have at least two points at which its tangent line is horizontal
True
If the velocity of an object is constant, then its acceleration is zero
True
If y is a differentiable function of u, u is a differentiable function of v, and v is a differentiable function of x, then dy/dx=(dy/du)(du/dv)(dv/dx)
True
If y is differentiable, then lim∆x→0(∆y-dy)=0
True
If y=(x+1)(x+2)(x+3)(x+4), then d⁵y/dx⁵=0
True
If y=ax+b, then ∆y/∆x = dy/dx
True
If y=x+c, then dy=dx
True
If y=x/π, then dy/dx = 1/π
True
If ∫'(c) and g'(c) are zero and h(x)=∫(x)g(x), then h'(c)=0
True
If ∫(x) = g(x)+c, then ∫'(x) = g'(x)
True
If ∫(x) is an nth-degree polynomial, then f^(n+1)(x)=0
True
If ∫(x)=ax³+b and ∫ is increasing on (-1,1), then a > 0
True
The average rate of change approaches the instantaneous rate of change as ∆x approaches zero
True
The average rate of change can be equal to the instantaneous rate of change
True
The average rate of change of y with respect to x is given by ∆y/∆x = ∫(x+∆x)-∫(x)/∆x
True
The equation x²+y²=r² IMPLICITLY defines y as a function of x
True
The equation x³+y³=r³ IMPLICITLY defines y as a function of x
True
The equation y=ax+b EXPLICITLY defines y as a function of x
True
The functions given by ∫(x)=x² and g(x)=x²+2 have the same derivative
True
The graph of every cubic polynomial has precisely one point of inflection
True
The second derivative represents the rate of change of the first derivative
True
The slope of the graph of y=x² is different at every point on the curve
True
The sum of two increasing functions is increasing
True
The tangent function is differentiable at every point in its domain
True
