Kali Thomas

2022-04-10

What is the equation of the line tangent to $f\left(x\right)=2{x}^{3}+8x$ at x=1

tempur8x43

Beginner2022-04-11Added 16 answers

Explanation:

The equation of the tangent line is: y=kx+n

where$k={f}^{\prime}\left({x}_{0}\right),{x}_{0}=1$

So,${f}^{\prime}\left(x\right)={(2{x}^{3}+8x)}^{\prime}=6{x}^{2}+8,$

and hence$k={f}^{\prime}\left(1\right)=6\cdot {1}^{2}+8=14$

We have:$f\left({x}_{0}\right)=f\left(1\right)=2\cdot {1}^{3}+8\cdot 1=10$ and

$y\left({x}_{0}\right)=k{x}_{0}+n$

$10=14\cdot 1+n\Rightarrow n=-4$

Finally, y=14x-4

The equation of the tangent line is: y=kx+n

where

So,

and hence

We have:

Finally, y=14x-4

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

$f(x,y)={x}^{3}-6xy+8{y}^{3}$ $\frac{1}{\mathrm{sec}(x)}$ in derivative?

What is the derivative of $\mathrm{ln}(x+1)$?

What is the limit of $e}^{-x$ as $x\to \infty$?

What is the derivative of $f\left(x\right)={5}^{\mathrm{ln}x}$?

What is the derivative of $e}^{-2x$?

How to find $lim\frac{{e}^{t}-1}{t}$ as $t\to 0$ using l'Hospital's Rule?

What is the integral of $\sqrt{9-{x}^{2}}$?

What is the derivative of $f\left(x\right)=\mathrm{ln}\left[{x}^{9}{(x+3)}^{6}{({x}^{2}+7)}^{5}\right]$ ?

What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?

How to find the derivative of $y={e}^{5x}$?

How to evaluate the limit $\frac{\mathrm{sin}\left(5x\right)}{x}$ as x approaches 0?

How to find derivatives of parametric functions?

What is the antiderivative of $-5{e}^{x-1}$?

How to evaluate: indefinite integral $\frac{1+x}{1+{x}^{2}}dx$?