tangent of x^2 at a — step-by-step solution

Find the tangent at

x = a

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 f(

a

)

The point of tangency is (

a

a^{2}

)

Compute f'(

a

)

The slope is f'(

a

) =

2 a

The tangent passes through this point with this slope:

y = 2 a \cdot (x - a) + a^{2}

Compute the y-intercept:

b = a^{2} - 2 a \cdot a

a^{2} - 2 a \cdot a

ⓘ Multiplying powers with the same base adds the exponents:

a \cdot a

a^{2}

a^{2} - 2 a^{2}

ⓘ Like terms are grouped by adding their coefficients:

a^{2} - 2 a^{2}

- a^{2}

- a^{2}

▶Tangent line:

y = 2 a x - a^{2}