How do you find the value of c guaranteed by the mean value theorem if it can be applied for #f(x) = x^2 + 4x + 2# on the interval [-3,-2]?

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Answer 1 · 2015-04-16T15:39:51

Given #f(x) = x^2+4x+2#

The mean value theorem says that
there exists a value #c epsilon [-3,-2]#
such that
#f'(c) = (f(-3) - f(-2))/((-3)-(-2)) = -1#

#f'(x) = 2x+4#

so
#f'(c)= 2c+4 = -1#

#c = -2 1/2#
which is in the range #[-3,-2]#