What is the tangent of f(x)=5x^{1/2}+x^{3/2},\at x=4 ?

The tangent of f(x)=5x^{1/2}+x^{3/2},\at x=4 is y= 17/4 x+1

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tangent of f(x)=5x^{1/2}+x^{3/2},\at x=4

tangent of

f (x) = 5 x^{\frac{1}{2}} + x^{\frac{3}{2}}, at x = 4

y = \frac{17}{4} x + 1

Solution steps

Find the tangent point:

(4, 18)

Find the slope of

f (x) = 5 x^{\frac{1}{2}} + x^{\frac{3}{2}} : \frac{df ( x )}{d x} = \frac{5}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{17}{4}

Find the line with slope m=

\frac{17}{4}

and passing through

(4, 18) : y = \frac{17}{4} x + 1

y = \frac{17}{4} x + 1

\frac{d y}{d x}, y^{3} + y = x

\int \frac{1}{x ^{13}} d x

\int sec (x) \cdot tan (x) d x

\int (3 x^{2} - 6 x + 2) d x

f (x) = 2 - 5 x^{2}, (- 2, - 18)

What is the tangent of f(x)=5x^{1/2}+x^{3/2},\at x=4 ?
The tangent of f(x)=5x^{1/2}+x^{3/2},\at x=4 is y= 17/4 x+1