Can a function have two tangent lines?

But the first derivative only gives one slope. For two lines with the same slope to be distinct, they must be parallel. A function is either differentiable at a point, which means there is one tangent line, or the function is not differentiable, which means there can be any number of tangents.

How do you find the derivative of a function with two points on a graph?

Choose a point on the graph to find the value of the derivative at. Draw a straight line tangent to the curve of the graph at this point. Take the slope of this line to find the value of the derivative at your chosen point on the graph.

How do you find the derivative of a tangent line?

1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f ‘(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

How do you find where two tangent lines are parallel?

To be parallel, two lines must have the same slope. The slope of the tangent line at a point of the parabola is given by the derivative of y=x2−3x−5. This means that the question is asking at what point the derivative of the parabola will equal the slope of 3x−y=2.

What is the derivative of tangent?

sec2x
The derivative of tan x is sec2x. When the tangent argument is itself a function of x, then we use the chain rule to find the result.

How do you find the derivative at a point?

To find the derivative at a point we can draw the tangent line to the graph of a cubic function at that point: But how can we draw a tangent line?. We can use a magnifying glass!. If we look very near the point in the graph of the function we can see how the function resembles the tangent line.

What is the derivative of the function with a horizontal tangent?

The derivative is zero where the function has a horizontal tangent. Use the following graph of to sketch a graph of . The solution is shown in the following graph. Observe that is increasing and on . Also, is decreasing and on and on . Also note that has horizontal tangents at -2 and 3, and and .

What is the derivative of a cubic function of degree 3?

Polynomials of degree 3 are cubic functions. A real cubic function always crosses the x-axis at least once. The derivative of a function at a point can be defined as the instantaneous rate of change or as the slope of the tangent line to the graph of the function at this point.

Is the derivative of a function decreasing convexly at two points?

At two points the derivative is taken and it is noted that at both f’ < 0. In other words, f is decreasing. Figure d shows a function decreasing convexly from (a, f (a)) to (b, f (b)).