A point in the first quadrant satisfies

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A point (x,y)(x,y) in the first quadrant satisfies x2+y2=25x^{2}+y^{2}=25. Define F(x)=∫0y(3t−t2) dt.F(x)=\int_{0}^{y} \bigl(3t-t^{2}\bigr)\,dt. Find dFdx\dfrac{dF}{dx} at x=3x=3.

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