tangent g(x)=x^2 at x=1 — step-by-step solution

Find the tangent at

x = 1

Let's perform the differentiation:

\frac{d}{d x} (x^{2})

ⓘ The derivative of x^n is n*x^(n-1):

\frac{d}{d x} (x^{2})

2 x

2 x

Compute g(

1

)

1^{2}

1

The point of tangency is (

1

1

)

Compute g'(

1

)

2 \cdot 1

2

The slope is g'(

1

) =

2

The tangent passes through this point with this slope:

y = 2 \cdot (x - 1) + 1

Compute the y-intercept:

b = 1 - 2

1 - 2

ⓘ Start from

1

and move back

2

on the number line, going below zero:

1 - 2

-1

-1

▶Tangent line:

y = 2 x - 1