# Thread: can someone help me with this question

1. ## can someone help me with this question

sketch the graph of y =x^4 +3 (done this)
2. show that y = 4x is a tangent to this curve and find the point of contact
3. sketch this tangent on your original set of axis
please someone tell me what to do

2. Originally Posted by kayla220220
sketch the graph of y =x^4 +3 (done this)
2. show that y = 4x is a tangent to this curve and find the point of contact
3. sketch this tangent on your original set of axis
please someone tell me what to do
Taking the derivative of the function gives us $y'=4x^3$. Now the line $y=4x$ has slope $4$, so we want to find which $x$ will give us $y'=4$. Solving for $x$:

$4x^3=4 \implies x=1$

So the point of contact is $x=1$ (and $y=4$).