MTH 241 Midterm Study Guide
Use the graph to find limx->-1 when f(x)=1/x+1
As x approaches -1 from either side, they do not equal, therefore, the limit doesn't exist
Below is a table of revenue in thousands of dollars for the first 10 days a new product is on the market. What was the average rate of change of revenue from day 3 to day 9?
Average rate of change: (y2-y1)/(x2-x1), when the points are (9, 7.34) and (3, 4.82)
A line has a slope of -4/5 and goes through the point (12,−7). Which of the following points must the line also go through?
Use the slope formula and the existing points to find the same slope
Find the Limit
1. factor the numerator and denominator 2. cancel any common factors 3. plug in the limit and evaluate
What is the difference quotient for the function f x = -2x^2+x
Do not approach 0 with h during these questions. When canceling out a single h, remember to keep the 1.
Find the equation of the line that is tangent to the graph of f(x)=4/x^2 at the point (−1,4).
Find the derivative then input the x-value into the found equation. This is the slope. Put in point-slope form then rearrange into slope-intercept form
The height s (in feet) of an object fired straight up from ground level with an initial velocity of 150 feet per second is given by s=-16t^2+150t, where t is time in seconds. How fast is the object moving after 5 seconds?
Find the derivative, s'(x). Then input 5 input the derivative function.
If f(x)=5x^2+13x-1/x then f ''(−1) = ?
Find the first derivative. Find the second derivative Input -1 into the x place for the second derivative
The position equation for the movement of a particle is given by (t^2-1)^3 , where s is measured in feet and t is measured in seconds. Find the acceleration of the particle at time t = 2 seconds.
Find the second derivative and input value
Find all the critical numbers for
Find when f'(x) equals zero
Find the critical number(s) for the function
Find when f'(x) equals zero
Given the graph of a line, find the line's equation.
First find where the line crosses the y-axis, for this it is 7. Then find where the you can find the slope. I used the where the line crosses the x-axis.
Find the equation for the straight line that goes through the points (2, -1) and (-3, 1)
First use the two points to find the slope. Next, use one of the points to form a point-slope form equation. It doesn't matter which one, they will result in the same end answer. Finally, transform the point-slope form equation into the slope-intercept form.
Given the graph of y = r(x), we can see that r(x) < 0 and r'(x) > 0 at the point labeled:
Look for the negative y-values. Then look where the graph is increasing
Find the slope of the line with equation 12y − 9x −13 = 5
Rearrange the equation to get to y=mx+b form
Find the equation of the line that goes through (-6, 14) and is perpendicular to the line − 8y + 6x −13 = 0
Rearrange the existing equation to make y=mx+b. The slope of the perpendicular line will be the negative reciprocal of the existing equation. Then use the points given to find the new equation.
Find all the points at which the graph of f(x)=-x^3+3x^2-2 has horizontal tangent lines.
Take the derivative, set equal to zero to find x-values. Input those values in the f(x) equations to find the y-values
If y = f (x) is a differentiable function, then f'(6/5)= -7/8 means:
The first derivative is the slope of the equation.
What is the equation of the line that goes through the point (-1/2,5) with a slope of (4/9)?
Use point-slope form, y-y1=m(x-x1), to discover the first. Then use algebra to transfer to slope-intercept form, y=mx+b.
A business had an annual retail sales of $100,000 in 1991 and $226,000 in 1994. Assuming that the annual sales followed a linear pattern, what were the retail sales in 1993?
Use the ARC formula to find how much the price rises per year. Since we want the value for 1993, we will simply subtract the found value from the value of 1994.
If f(x)=2x^2+4, then which of the following will correctly calculate the derivative of f(x) ?
Use the difference quotient
