What is the tangent of f(x)=16-7e^x ?

The tangent of f(x)=16-7e^x is y=-7e^{a_{0}}x+16-7e^{a_{0}}+7a_{0}e^{a_{0}}

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tangent of f(x)=16-7e^x

tangent of

f (x) = 16 - 7 e^{x}

y = - 7 e^{a_{0}} x + 16 - 7 e^{a_{0}} + 7 a_{0} e^{a_{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 16 - 7 e^{a_{0}})

Find the slope of

f (x) = 16 - 7 e^{x} : \frac{df ( x )}{d x} = - 7 e^{x}

Compute the slope of

f (x) = 16 - 7 e^{x}

x = a_{0} : m = - 7 e^{a_{0}}

Find the line with slope m=

- 7 e^{a_{0}}

and passing through

(a_{0}, 16 - 7 e^{a_{0}}) : y = - 7 e^{a_{0}} x + 16 - 7 e^{a_{0}} + 7 a_{0} e^{a_{0}}

y = - 7 e^{a_{0}} x + 16 - 7 e^{a_{0}} + 7 a_{0} e^{a_{0}}

\int sin (a) x d x

\frac{1}{s ^{2} + 3 s + 2}

\frac{d}{d x} (4 sec (5 x))

f (t) = \frac{t ^{2}}{t ^{3} + 1}

\frac{d}{d x} (2 arctanh (x))

What is the tangent of f(x)=16-7e^x ?
The tangent of f(x)=16-7e^x is y=-7e^{a_{0}}x+16-7e^{a_{0}}+7a_{0}e^{a_{0}}