Solved: "What is the equation of the line tangent..."

Mina Whitehead

Answered question

2022-04-09

What is the equation of the line tangent to

f (x) = 5 x^{2} - 3 x + 2

at x=3?

Answer & Explanation

glajusv8iv

Beginner2022-04-10Added 10 answers

Explanation:
We can write the equation in slope-intercept form y = mx +c
where m represents the gradient and c , the y-intercept.
The value of f'(3) is equal to m and c may be found by evaluating f(3)

f (x) = 5 x^{2} - 3 x + 2

\Rightarrow f^{'} (x) = 10 x - 3

and f'(3)=10(3)-3=27=m (gradient of tangent)
Partial equation is therefore : y = 27x +c
now

f (3) = 5 {(3)}^{2} - 3 (3) + 2 = 38

hence (3 ,38) is a point on the tangent and substituting this into the partial equation will give us the value of c.

x = 3, y = 38 : 38 = 81 + c \to c = - 43

Thus the equation of tangent is y=27x-43

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