Show that the curve y = 4 x 3 + 7 x − 5 y=4x3+7x-5 has no tangent line with slope 2 2. y = 4 x 3 + 7 x − 5 ⇒ m = y ' = y=4x3+7x-5⇒m=y′= Preview , but x 2 x2 0 0 for all x x, so m ≥ m≥ for all x x.

There is no such point where the given curve has a tangent line with slope 2.

Step-by-step explanation:

We have been given a curve . We are asked to show that the given curve has no tangent line with slope 2.

First of all, we will find the derivative of given curve as shown below:

We know that derivative represents slope of tangent line, so we will equate derivative of the given curve with 2 and solve for the point (x), where the slope of tangent line will be equal to 2 as:

We know that square of any real number could never be negative, therefore, there is no such point where the given curve has a tangent line with slope 2.