Find an equation for the tangent line to the function $f(x)=(1+x^{\frac{3}{2}})^3$ through the point $(1,8)$.
I really have no idea how to attack this problem.
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The slope at $x=1$ is $f'(1)$. $$f'(x)= 9/2 \sqrt{x} (x^{3/2}+1)^2 ->f'(1)=18$$ equation of the line tangent to the $f(x)$ at $(1,8)$: $$y-y_{0}=f'(1).(x-x_{0})=y-8=18(x-1)$$ so $$y=18x-10$$.
Ömer
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The slope of the line is $f'(1)$, the deriviative of $f$ at $1$. So the line will have equation $y=f'(1)x+c$ for some $c$. The line has to pass through $(1,8)$, so substituting $x=1$ and $y=8$ lets you solve for $c$.
mdp
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