tangent of t^2 at 2 — step-by-step solution

Find the tangent at

t = 2

Let's perform the differentiation:

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

ⓘ The derivative of x^n is n*x^(n-1):

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

2 t

2 t

Compute f(

2

)

2^{2}

ⓘ An integer power is a repeated product:

2^{2}

2 \cdot 2

4

4

The point of tangency is (

2

4

)

Compute f'(

2

)

2 \cdot 2

ⅰ

2 \cdot 2

4

4

The slope is f'(

2

) =

4

The tangent passes through this point with this slope:

y = 4 \cdot (t - 2) + 4

Compute the y-intercept:

b = 4 - 4 \cdot 2

4 - 4 \cdot 2

ⓘ Multiplications are done before additions and subtractions:

4 \cdot 2

8

4 - 8

ⓘ Start from

4

and move back

8

on the number line, going below zero:

4 - 8

-4

-4

▶Tangent line:

y = 4 t - 4