Question

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

f(x)=x²+1

Answer 1

$f(x) =x^2+1$

we start by finding the derivative of the function f(x)by applying the sum rule.

$d/dx(f(x))=d/dx(x^2)+d/dx(1)$

=2$x$

The equation for the slope of the tangent line will be the derivative of f(x)

which is $2x$.

the equation of the line is given by the following equation

$y=mx+c$

where m is the slope of the tangent and c is a constant.

y=2x

therefore the slope of this equation is 2.

The slope of the tangent line for the given equation is 2.