SOLUTION: Find the gradient of f(x) at x=4 for which f(x)=(5(x-1)(x-5))/8x^1/2

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Question 1187895: Find the gradient of f(x) at x=4 for which f(x)=(5(x-1)(x-5))/8x^1/2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the gradient of f%28x%29 at x=4 for which f%28x%29=%285%28x-1%29%28x-5%29%29%2F%288x%5E%281%2F2%29%29 or f%28x%29=%285%28x-1%29%28x-5%29%29%2F%288sqrt%28x%29%29

The gradient (slope) of a curve of f%28x%29 at x=a+is f'%28a%29

By taking the derivative, '%28x%29+=+%285+%283+x%5E2+-+6+x+-+5%29%29%2F%2816+x%5E%283%2F2%29%29

By plugging in x=4 we get

f'%284%29+=+%285+%283%2A4%5E2+-+6%2A4+-+5%29%29%2F%2816%2A4%5E%283%2F2%29%29
f'%284%29+=+95%2F128

Hence, the gradient is 95%2F128+ (exact solution) approximately 0.7421875