help pleaseeee !! Consider the function f(x)=1−6x^2 on the interval [−5,4].

Question

Consider the function f(x)=1−6x^2 on the interval [−5,4].

(A) Find the average value of the function on this interval, i.e.

f(4)−f(−5) / 4−(−5)= ....

(B) By the Mean Value Theorem, we know there exists a c in the open interval (−5,4) such that f′(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

c = ....

Answer 1

f(4) = 1 - 6*4 *4 = - 95

f(-5) = 1 - 6 (-5)(-5) = -149

average value of function = -95 - (-149) 54

------------------- = ------- = 6

4 - (-5) 9

b) mean value theorem

f'(x) = d/dx (1- 6x^2) = -12x

f'(c) = -12c

-12c = 6

c= -1/2