What is the tangent of f(x)=4sin(x),\at x= pi/4 ?

The tangent of f(x)=4sin(x),\at x= pi/4 is y=2sqrt(2)x+2sqrt(2)-pi/(sqrt(2))

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tangent of f(x)=4sin(x),\at x= pi/4

tangent of

f (x) = 4 sin (x), at x = \frac{π}{4}

y = 22 x + 22 - \frac{π}{2}

Solution steps

Find the tangent point:

(\frac{π}{4}, 22)

Find the slope of

f (x) = 4 sin (x) : \frac{df ( x )}{d x} = 4 cos (x)

Compute the slope of

f (x) = 4 sin (x)

x = \frac{π}{4} : m = 22

Find the line with slope m=

22

and passing through

(\frac{π}{4}, 22) : y = 22 x + 22 - \frac{π}{2}

y = 22 x + 22 - \frac{π}{2}

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

\frac{d}{d x} (sin^{x} (x))

f (x) = 5 x - 9 x^{2}, at x = 1

\frac{d}{d x} (- 8 cos (x))

e^{x} x + 2 e^{x}

What is the tangent of f(x)=4sin(x),\at x= pi/4 ?
The tangent of f(x)=4sin(x),\at x= pi/4 is y=2sqrt(2)x+2sqrt(2)-pi/(sqrt(2))