Consider the function f(x)=10sqrrootx+5 on the interval [3,10].

Question

i found the average slope to be 2.043181217
By the Mean Value Theorem, we know there exists a c in the open interval (3,10) such that f'(c) is equal to this mean slope

i tried tking the first derivative of the eq and getting x^1/2+5/x^1/2 +2.043181217

please help i don't no wut to do next?

Answer 1

Lets check your slope.


f'=5/sqrtx
2.043=5/sqrtx
sqrtx=2.44
x=5.97

check that.