Question

If y = 2 Superscript x squared + 2, which of the following gives the slope of the tangent line for all values of x?

(ln 2)(2 Superscript x squared + 2)
2x(ln 2)(2 Superscript x squared + 2)
(x2 + 2)(2 Superscript x squared + 1)
(x2 + 2)(ln 2)(2 Superscript x squared + 1)

Answer 1

The slope of the tangent line to the graph of the function y = 2x2 + 2 for all values of x is represented by the expression 2x(ln 2)(2x2). Therefore correct option is B

Step-by-step explanation:

The student is asking for the slope of the tangent line to the graph of the function y = 2x2 + 2 at any value of x.

To find this, we need to differentiate the function with respect to x using the chain rule and the properties of exponents and logarithms.

First, let's write the function as y = eln(2)x2 + 2 because 2 can be written as eln(2).

Now, we apply the chain rule: dy/dx = eln(2)x2 ⋅ (ln(2) ⋅ 2x), which simplifies to dy/dx = 2x(ln(2))(2x2).

Thus, 2x(ln 2)(2x2) is the correct expression for the slope of the tangent for all values of x.