"How do you find the equation of the..." solved and explained

daurialebraslmc

Answered question

2022-04-13

How do you find the equation of the tangent line to the curve

3 x^{2} - 5 x + 2

at x=3?

Answer & Explanation

Emily Green

Beginner2022-04-14Added 14 answers

First, let's find the value of y for (3,y) to be on the graph of the function.

y = 3 {(3)}^{2} - 5 (3) + 2

y=27-15+2
y=14
Next, differentiate using the power rule. Let your function be f(x), then:
f'(x)=6x-5
Now, plugging in our value of x to find the slope:
f'(3)=6(3)-5
f'(3)=13

∴

The slope of the tangent is 13. Now we know a point on the original function
(3, 14) and the slope of the tangent, 13.
We will use point slope form to determine the equation of the tangent.

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

y-14=13(x-3)
y-14=13x-39
y=13x-25

∴

The equation of the tangent is y=13-25.

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