Consider the function $f(x)=9x^2 +7x$
The derivative is $f'(x)=18x+7$
The slope of the tangent to the graph of $f(x)$ at $x=2$ is $43$
The equation for the tangent line at $x=2$ is $y=43x-36$
I found all of these answers, but when I get to the last question, I don't know how to solve it. Can anyone tell me how to find it?
The value of $x$ where the tangent line to $f(x)$ is horizontal is $x=?$
Thank you!
$\endgroup$2 Answers
$\begingroup$when the tangent line is horizontal, the $y'=0$ then $$18x+7=0$$ $$x=-\frac{7}{18}$$
$\endgroup$ 2 $\begingroup$An horizontal line has a slope equal to zero, so the tangent line at the point of abscissa $x$ is horizontal if and only if $f'(x) = 0$.
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