What is the tangent of f(x)=3^x,\at x=1 ?

The tangent of f(x)=3^x,\at x=1 is y=3ln(3)x+3-3ln(3)

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tangent of f(x)=3^x,\at x=1

tangent of

f (x) = 3^{x}, at x = 1

y = 3 ln (3) x + 3 - 3 ln (3)

Solution steps

Find the tangent point:

(1, 3)

Find the slope of

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

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 = 3 ln (3)

Find the line with slope m=

3 ln (3)

and passing through

(1, 3) : y = 3 ln (3) x + 3 - 3 ln (3)

y = 3 ln (3) x + 3 - 3 ln (3)

\int_{1}^{e} \frac{2 x - 3 x ^{3}}{x ^{2}} d x

f (x) = x^{2} + 4 x

f (x) = 2 x - cot^{2} (x)

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

f (x) = 1260 - 16 x^{2}, at x = 3

What is the tangent of f(x)=3^x,\at x=1 ?
The tangent of f(x)=3^x,\at x=1 is y=3ln(3)x+3-3ln(3)