More Review for Flashcard 3.1-3.3

Front

Find the equation of the tangent line of y = 2x^3 + 3x^2 - 12x + 1 when x = -2

Back

y = 9

Front

Find the derivative of the function f(x) = 3x^2 - 2x + 5.

Back

f'(x) = 6x - 2.

Front

Given that y = (x + 2)/(x - 3), find y'.

Back

y' = -5/(x - 3)^2

Front

Solve for the equation of the tangent line to the function k(x) = x^2 + 3x - 2 at the point (1, 2).

Back

The equation of the tangent line is y = 5x - 3.

Front

Given the function n(x) = 3x^3 - 2x^2 + 5x - 1, find the coordinates of the point where the tangent line is horizontal.

Back

The coordinates of the point where the tangent line is horizontal are (1, 5).

Front

What is the definition of a tangent line?

Back

A tangent line to a curve at a given point is the straight line that just touches the curve at that point, having the same slope as the curve at that point.

Front

What is the derivative of a function?

Back

The derivative of a function represents the rate of change of the function with respect to its variable.

Front

How do you find the slope of a tangent line at a point on a curve?

Back

To find the slope of the tangent line at a point, calculate the derivative of the function and evaluate it at that point.

Front

What does it mean for a tangent line to be horizontal?

Back

A tangent line is horizontal when its slope is zero, indicating that the function has a local maximum or minimum at that point.

Front

What is the power rule for differentiation?

Back

The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).