Question

Note: y^1 means the deriviative of...

If f(2)=3 and y^1(2)=5 find an equation of the tangent line and the normal line to the graph of y=f(x) at the point where x=2.

Answer 1

"If f(2)=3..."
The point of tangency is (2,3).
f'(2)=5 means the slope is 5 at the point of tangency.
The equation of the tangent line is therefore a line with slope 5 that passes through (2,3).
The line passing through P1(x1,y1) with a slope of m is given by:
L : (y-y1)=m(x-x1)
In the case of the required tangent line:
L(tangent) : (y-3)=5(x-2)
L(tangent) : y=5x-7
The normal can be found similarly by replacing m by -1/m
L(normal) : (y-3)=-(1/5)(x-2)
y=-(1/5)x + 17/5

Please check my calculations.