A curve has equation y=f(x) and is such that f'(x)=3x^(1/2) + 3x^(-1/2) - 10.

Question

i. By using the substitution u=x^(1/2), or otherwise, find the values of x for which the curve y=f(x) has stationary points.

correct answer: 1/9 or 9

ii. Find f''(x) and hence, or otherwise, determine the nature of each stationary point.

correct answer: f''(x) = 3/2 x^(-1/2) - 3/2 x(-3/2) at x = 1/9 max, at x=9 min

iii. It is given that the curve y=f(x) passes through the point (4,-7). Find f(x).

correct answer: f(x)=2x^(3/2) + 6x^(1/2) - 10x + 5.

Answer 1

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