Derivatives (Power Rule)

Front

What is the Power Rule for derivatives?

Back

The Power Rule states that if f(x) = x^n, then the derivative f'(x) = n*x^(n-1).

Front

How do you determine where the slope of the tangent line is positive?

Back

The slope of the tangent line is positive where the derivative of the function is greater than zero.

Front

What is the derivative of f(x) = x^4?

Back

f'(x) = 4x^3.

Front

How do you find the equation of the normal line at a given point?

Back

To find the equation of the normal line, first find the slope of the tangent line at that point, then use the negative reciprocal of that slope for the normal line.

Front

What is the derivative of f(x) = x^3 + x^2 + 3?

Back

f'(x) = 3x^2 + 2x.

Front

What does dy/dx represent in calculus?

Back

dy/dx represents the derivative of y with respect to x, indicating the rate of change of y as x changes.

Front

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

Back

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

Front

What is the significance of the derivative in relation to a function's graph?

Back

The derivative indicates the slope of the function's graph at any given point, showing whether the function is increasing or decreasing.

Front

How do you apply the Power Rule to find the derivative of a polynomial function?

Back

For each term in the polynomial, apply the Power Rule by multiplying the coefficient by the exponent and then reducing the exponent by one.

Front

What is the normal line to a curve at a given point?

Back

The normal line is a line perpendicular to the tangent line at a given point on the curve.