How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=3x^2+2x+5# on the interval #[-1,1]# ?
1 Answer
May 2, 2018
# c=0 #
Explanation:
We seek to verify the Mean Value Theorem for the function
# f(x) = 3x^2+2x+5# on the interval#[-1,1]#
The Mean Value Theorem, tells us that if
# f'(c) = (f(b)-f(a))/(b-a) #
So, Differentiating wrt
# f'(x) = 6x+2 #
And we seek a value
# :. 6c+2 = ((3+2+5)-(3-2+5))/(2) #
# :. 6c + 2 = 4/2 #
# :. 6c + 2 = 2 #
# :. 6c = 0 #
# :. c=0 #