02.10 Differentiation: Definition and Fundamental Properties Exam Part One

Let m be the function given by What is the instantaneous rate of change of m with respect to x at x = 3?

- 1/9

Estimate f ′(−12) using the data in the table. x −13 −11 −9 −7 f(x) 1.02 1.05 1.12 1.14 i aint organizing that table, good luck for u tho

0.015

Which is equivalent to d over dt of 2 times sin t times cos t question mark

2cos2t − 2sin2t

Let h be a differentiable function with a tangent line at x = π. The equation of the tangent line is y = 0.3x − 0.1. What must be true about h and h′ at x = π? h(π) = 0.8425 h(0) = −0.1 h′(π) = 0.2

I only

a graph of a cubic function decreasing from the left and going to a local minimum at negative 1.333 comma 0.815 and then increasing to a local maximum at 0 comma 2 and then decreasing The graph of the function f(x) is shown. Which of the following could be the graph of f ′(x)?

a graph of a parabolic function increasing from the left and going to a local maximum at negative 0.667 comma 1.333 and then decreasing to the right

Let f be the function defined by f(t) = et − 1. Which of the following represents the average rate of change of f on the interval [2, 4]?

e to the fourth power minus e squared all over 2

Let f be the function defined by f(x) = |x + 2| for all x. Which of the following statements is true?

f is continuous but not differentiable at x = −2

Find g′(1) if g of x is equal to 5 times x cubed minus 6 times x squared plus 8 times x plus the square root of 8 period

g′(1) = 11

Differentiate y with respect to x given y equals the square root of x times the quantity 4 plus b times x to the fifth power period

quantity 11 times b times x to the fifth power plus 4 close quantity over the quantity 2 times the square root of x

It is given that f of x equals 1 over the quantity 2 times x comma and g of x equals 1 over the quantity 3 times x plus c period Find some integer c such that d over dx at x equals 1 of the quantity f over g close quantity equals 2 period

−4