How do you find the equation of the line tangent

ebnspmia0jj

ebnspmia0jj

Answered question

2022-02-12

How do you find the equation of the line tangent to the graph of f(x)=x4+2x2?

Answer & Explanation

Michaela Boyle

Michaela Boyle

Beginner2022-02-13Added 10 answers

Explanation:
If f(x) is continuous and differentiable at x1, then the equation of the line tangent to f(x) at (x1,f(x1)) in point slope form is:
yf(x1)=f(x1)(xx1)
Add f(x1) to both sides to get:
y=f(x1)x+(f(x1)x1f(x))
In our example, f(x)=x4+2x2 so
f(x)=4x3+4x=4x(x2+1)
and the equation of the tangent in slope intercept form is:
y=4x1(x12+1)x+((x14+2x12)x1(4x13+4x1))
=4x1(x12+1)xx12(3x12+2)

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