Tangent & Normal Lines (6-2)

Front

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

Back

y=2x-1

Front

When we 'take the derivative' of a function what are we finding?

Back

The slope of the tangent line

Front

Find the slope at x = 3 of the equation f(x) = 3x²

Back

18

Front

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

Back

-1/3

Front

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

Back

y = 2x - 1

Front

Define a tangent line in relation to a curve.

Back

A tangent line is a straight line that touches a curve at a single point without crossing it.

Front

What is the relationship between the derivative and the slope of a tangent line?

Back

The derivative of a function at a point gives the slope of the tangent line at that point.

Front

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

Back

Take the derivative of the function and evaluate it at the given point.

Front

What is the formula for the slope of a line?

Back

Slope (m) = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2).

Front

What is a normal line in relation to a curve?

Back

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