Contact Info

Math Asked by a SnapAndSolve user · about 2 hours ago

Write an equation of the line tangent to the graph of f(x) = 2x^3 - x^2 + 3x at the point where x = 1.

Write an equation of the line tangent to the graph of f(x) = 2x^3 - x^2 + 3x at the point where x = 1.

Answer

To find the equation of the tangent line, we need to determine the derivative of f(x) and evaluate it at x = 1 to find the slope of the tangent line.

Find the derivative of f(x):
f(x) = 2x^3 - x^2 + 3x
f'(x) = 6x^2 - 2x + 3
Evaluate f'(x) at x = 1:
f'(1) = 6(1)^2 - 2(1) + 3 = 6 - 2 + 3 = 7
Find the y-coordinate of the point on the graph at x = 1:
f(1) = 2(1)^3 - (1)^2 + 3(1) = 2 - 1 + 3 = 4
Use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
y - 4 = 7(x - 1)
Simplify the equation:
y = 7x - 7 + 4
y = 7x - 3

The equation of the tangent line is y = 7x - 3.

Have a similar question?

Snap a photo of your homework and get a step-by-step answer in seconds. You can ask follow-up questions until it makes sense.

Solve my question free Math help

More math questions

© 2026 SnapAndSolve