What is the tangent of f(x)=(x^3)/2 ,(5,62.5) ?

The tangent of f(x)=(x^3)/2 ,(5,62.5) is y= 75/2 x-125

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tangent of f(x)=(x^3)/2 ,(5,62.5)

tangent of

f (x) = \frac{x ^{3}}{2}, (5, 62.5)

y = \frac{75}{2} x - 125

Solution steps

Find the slope of

f (x) = \frac{x ^{3}}{2} : \frac{df ( x )}{d x} = \frac{3 x ^{2}}{2}

Compute the slope of

f (x) = \frac{x ^{3}}{2}

(5, 62.5) : m = \frac{75}{2}

Find the line with slope m=

\frac{75}{2}

and passing through

(5, 62.5) : y = \frac{75}{2} x - 125

y = \frac{75}{2} x - 125

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What is the tangent of f(x)=(x^3)/2 ,(5,62.5) ?
The tangent of f(x)=(x^3)/2 ,(5,62.5) is y= 75/2 x-125