Question

et f(x) = 5 x^2 + 4 x - 8. Answer the following questions.
1. Find the average slope of the function f on the interval [-1,1].
Average Slope:= ___________
2. Verify the Mean Value Theorem by finding a number c in (-1,1) such that f'(c) = __________
Answer: c =

Answer 1

so once you have th answer to part 1 above you need

f'(x) = 10x + 4

so

f'(c) = 10c + 4

applying the mean value theorem you have


\[f'(c) = \frac{f(1) - f(-1)}{1 - (-1)} \]

which means

\[10c + 4 = \frac{f(1) - f(-1)}{1 - (-1)}\]

now just solve for c

Answer 2

and for part 1 you should get

f(-1) = 5 - 4 - 8 = -7

f(1) = 5 + 4 - 8 = 1

so using

\[avg..slope = \frac{f(1) - f(-1)}{1 - (-1)}\]

\[Avg.. slope = \frac{1 --7}{1 - -1}\]

then you find the average slope is

Avg Slope = 4

Answer 3

Thanks for the help it makes more sense now :)

Answer 4

sorry that I did it back the front... but I'm glad it makes sense