Answer to Question #1863 in Calculus for Abhilsh

Question

Find the number c that satisfies the conclusion of Rolle's Theorem.

f(x)= √(x ) - 1/3 x

[0, 9]

Answer 1

f(0) = 0 - 1/3*0 = 0;
f(9) = 3 - 1/3*9 = 0.
Let's find the point where the first derivative is equal to zero:
f'(x) = 1/(2√x) - 1/3 = 0
3 - 2√x = 0, & x<>0
√x = 3/2;
x = 2.25.

c = 2.25