What is the tangent of f(x)=5sqrt(x),\at x=4,x=9 ?

The tangent of f(x)=5sqrt(x),\at x=4,x=9 is y= 5/4 x+5

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tangent of f(x)=5sqrt(x),\at x=4,x=9

tangent of

f (x) = 5 x, at x = 4, x = 9

y = \frac{5}{4} x + 5

Solution steps

Find the tangent point:

(4, 10)

Find the slope of

f (x) = 5 x : \frac{df ( x )}{d x} = \frac{5}{2 x}

Compute the slope of

f (x) = 5 x

x = 4 : m = \frac{5}{4}

Find the line with slope m=

\frac{5}{4}

and passing through

(4, 10) : y = \frac{5}{4} x + 5

y = \frac{5}{4} x + 5

x \to - 3 - lim (\frac{3 - x}{9 - x ^{2}})

f (x) = 4 x^{\frac{3}{2}}

ln (1 - x), 0

\int x (3 x + 1)^{7} d x

What is the tangent of f(x)=5sqrt(x),\at x=4,x=9 ?
The tangent of f(x)=5sqrt(x),\at x=4,x=9 is y= 5/4 x+5