# How do you find the slope of the tangent line to the graph of the function #h(t)=t^2+3# at (-2,7)?

##### 1 Answer

Jun 30, 2017

The equation of the tangent is -

#y=-4x-1#

#### Explanation:

Given -

#h(t)=t^2+3#

Let us have it as -

#y=t^2+3#

Its slope at any point is given by its first derivative.

#dy/dx=2t#

Slope of the curve exactly at

#dy/dx=2(-2)=-4#

The tangent is passing through the point

The slope of the tangent at Point

#m=-4#

#x=-2#

#y=7#

#mx+c=y#

#(-4)(-2)+c=7#

#8+c=7#

#c=7-8=-1#

The equation of the tangent is -

#y=-4x-1#