JEE Advance - Mathematics (2005 - No. 6)
$$f(x)$$ is a differentiable function and $$g(x)$$ is a double differentiable
function such that $$\left| {f\left( x \right)} \right| \le 1$$ and $$f'(x)=g(x).$$
If $${f^2}\left( 0 \right) + {g^2}\left( 0 \right) = 9.$$ Prove that there exists some $$c \in \left( { - 3,3} \right)$$
such that $$g(c).g''(c)<0.$$
function such that $$\left| {f\left( x \right)} \right| \le 1$$ and $$f'(x)=g(x).$$
If $${f^2}\left( 0 \right) + {g^2}\left( 0 \right) = 9.$$ Prove that there exists some $$c \in \left( { - 3,3} \right)$$
such that $$g(c).g''(c)<0.$$
Rolle's Theorem
Mean Value Theorem
Intermediate Value Theorem
Taylor's Theorem
Extreme Value Theorem
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