Expert answers to "What is the equation of the tangent line..."

Kienastsrx

Answered question

2022-03-16

What is the equation of the tangent line of

f (x) = x^{2} - 2 x

at x=5?

Jarrett Chan

Beginner2022-03-17Added 6 answers

So at that point on the curve, as it is a tangent the gradient will be the same.
The gradient is calculated by differentiating.

\frac{d y}{d x} x^{2} - 2 x d x = \frac{1}{2} x - 2

We can then substitute x in to find the gradient at x=5.
Therefore,

\frac{1}{2} (5) - 2 = \frac{1}{2}

.
This is our gradient.
Then we need to find y at the point x=5.
Substitute into

x^{2} - 2 x

to get

{(5)}^{2} - 2 (5) = 15

.
Now we can use the equation of

y - y_{1} = m (x - x_{1})

.
Therefore:

y - 15 = \frac{1}{2} (x - 5)

Expand and rearrange:

y - 15 = \frac{1}{2} x - \frac{5}{2}

y = \frac{1}{2} x + \frac{25}{2}

2y=x+25.

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