2. Intro to Derivatives

Find the equation of the tangent line to the curve $y=\sin \left(x\right)+\cos \left(x\right)$ at the point $(0,1)$.

Given the function $f\left(x\right)=x^2+3x$, what is the slope of the line tangent to the curve at the point $x=2$?

Find an equation of the tangent line to the graph of $f\left(x\right)=x^2+2x$ at the point where $x=1$.

What is the slope of the tangent line to the curve $x^2+y^2=2$ at the point $(1,1)$?

For what value of $x$ is the tangent line to the function $f\left(x\right)=x^3-3x^2+2$ horizontal?

Find an equation of the tangent line to the curve $y=e^{x}cos\left(x\right)+sin\left(x\right)$ at the point $(0,1)$.

Derivatives and tangent lines

a. For the following functions and values of a, find f′(a).

f(x) = 8x; a = −3

Find an equation of the tangent plane to the surface $z=x^2+y^2$ at the point $(1,2,5)$.

Given the parametric equations $x=t^2-4$ and $y=t^2-2t$, find the equation of the tangent line to the curve at the point where $t=3$.

Find an equation of the line tangent to the following curves at the given value of x.

y = 4 sin x cos x; x = π/3

Find an equation of the tangent line to the curve $y=e^x$ at the point $(1,e)$.

What is the slope of the tangent line to the curve $y^3-x{y}^2+x^3=5$ at the point $(1,2)$?

Which of the following is an equation of the line tangent to the graph of $y=\cos x$ at $x=\frac{\pi }{2}$?

Given the function $f(x)=x^2+100$, calculate the slope of the tangent line at $x=0$.