Find an equation of the tangent line

Thread starter 10min
Start date Nov 30, 2008
Tags

Line Tangent Tangent line

In summary, the equation of a tangent line is a linear equation in the form y = mx + b, where m is the slope of the tangent line and b is the y-intercept. To find the equation of the tangent line, you need to know the slope and a point on the line. The slope can be found by taking the derivative of the original function at the given point. A tangent line can only intersect the original function at one point, while a secant line can intersect at two or more points. The equation of a tangent line can change at different points on the same curve due to the changing slope as the point moves along the curve.

Nov 30, 2008

10min

Homework Statement

Find an Equation of the tangent line to the curve y=10^x at the point (1,10)

Homework Equations

Derivative
y=mx+b

The Attempt at a Solution

I am totally lost
I don't know what to do with 10^x

Please help me
this will save me failing the class

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Nov 30, 2008

rock.freak667

Homework Helper

y=10^x
=> lny=xln10

Now just find dy/dx

FAQ: Find an equation of the tangent line

What is the equation of a tangent line?

The equation of a tangent line is a linear equation in the form y = mx + b, where m is the slope of the tangent line and b is the y-intercept.

How do you find the equation of the tangent line?

To find the equation of the tangent line, you need to know the slope and a point on the line. The slope can be found by taking the derivative of the original function at the given point. Then, use the point-slope formula to plug in the slope and point values to find the equation of the tangent line.

Can a tangent line intersect the original function at more than one point?

No, a tangent line can only intersect the original function at one point. This is because a tangent line is defined as a line that touches the curve at only one point and has the same slope as the curve at that point.

What is the difference between a tangent line and a secant line?

A tangent line touches the curve at only one point, while a secant line intersects the curve at two or more points. In other words, a tangent line is a special case of a secant line where the two points of intersection are the same.

Can the equation of a tangent line change at different points on the same curve?

Yes, the equation of a tangent line can change at different points on the same curve. This is because the slope of the tangent line is dependent on the point at which it is drawn, and the slope can change as the point moves along the curve.