Question

Let f(x)=5x2+5x−12. Answer the following questions.Find the average slope of the function f on the interval [−1,1].Verify the Mean Value Theorem by finding a number c in (−1,1) such that f′(c)=m¯¯¯.

Answer 1

the average slope is the slope of the line joining the two endpoints on the graph. Once you find that, the MVT says there is a c in the interval such that

f'(c) = that slope.

So, find that slope (call it m) and then just solve

f'(c) = 10c+5 = m