Question

Find the equation of the tangent line to each curve when x has a given value.

1. f(x)= x²+2 as x= 2

2.f(x)= 3x²+1 as x=1

Find the slope of the tangent line of the given function f below.

1.f(x)=2x+5

2.f(x)=x²-1

Answer 1

equation of the tangent line at the point $x_0$ is:

$y-y_0=y'(x_0)(x-x_0)$

1. f(2) = 6

$f'(x)=2x\implies f'(2)=4$

so, the equation of the given line is

$y-6=4(x-2)$

2. f(1) = 4

$f'(x)=6x\implies f'(1)=6$

so, the equation of the given line is

$y-4=6(x-1)$

The slope of the tangent line to a function f(x) is f'(x), so

1.f'(x) = 2

2.f'(x) = 2x