Equations of Tangent & Normal Lines

Front

What is a derivative?

Back

A derivative represents the slope of the tangent line to a function at a given point, indicating the rate of change of the function.

Front

What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=0?

Back

y=2x-1

Front

How do you find the slope of a function at a specific point?

Back

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

Front

What is the slope of the function f(x) = 3x² at x = 3?

Back

18

Front

What is the equation of the line tangent to the curve y = x² at x = 1?

Back

y = 2x - 1

Front

What is the slope of the line normal to the curve y = x² + x at x = 1?

Back

-1/3

Front

What does the slope of the tangent line represent?

Back

The slope of the tangent line represents the instantaneous rate of change of the function at a specific point.

Front

How do you find the equation of a tangent line?

Back

To find the equation of a tangent line, use the point-slope form: y - f(a) = f'(a)(x - a), where a is the point of tangency.

Front

What is the relationship between the slopes of tangent and normal lines?

Back

The slope of the normal line is the negative reciprocal of the slope of the tangent line.

Front

What is the derivative of f(x) = x²?

Back

f'(x) = 2x.