The figure shows graphs of f, f ', f '', and f '''. identify each curve.

f --> d

f' --> c

f'' --> b

f''' --> a

Step-by-step explanation:

The derivative of a function is another function which values are the slope of the line tangent to the curve at the point .

So the derivative at some point will be:

The curve has a steady decreasing rate when is close zero and has one local maximum and one local minimum where the slope of the tangent line should be zero. The curve shows this behaviour so we can say that is the derivative of .

The curve reach a minimum point when so the derivative should be zero at that point, with a decrasing rate for (negative derivative) and an increasing rate for (positive derivative). The curve shows this behaviour so we can say that is the derivative of .

The curve is constantly increasing, so its derivative is going to be always positive and has an inflection point in where the slope of the tangent line should be zero, then is the derivative of

Recapitulating:

Then:

f --> d

f' --> c

f'' --> b

f''' --> a

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

b) well because you get well