whats the correct answer for the first part Consider the equation below. f(x) =

Question

whats the correct answer for the first part

Consider the equation below. f(x) = 4x^3 + 21 x^2 - 294x + 4 Find the intervals on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) Find the local minimum and maximum values of f. local minimum value local maximum value Find the inflection point. (x, y) Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)

Explanation / Answer

f(x) = 4x3 + 21x2 - 294x + 4
f'(x) = 12x2 + 42x -294;

f(x) is increasing on the period where its derivative is >0
and decreasing on that period where its derivative is <0 ;
Thus f'(x) = 12x2 + 42x -294 which is a quadratic equation which opens upwards;

So this quadratice function is
<0 between its roots;
=0 at its roots and
>0 in all orther portion from - infinity to + infinity;

Finding its roots
12x2 + 42x -294 =0 which means
2x2+ 7x-49 =0
Thus x= [ -7 + or - sqrt(72 - 4(2)(-49) ) ] / 2*2
= [-7 + or - sqrt ( 441) ] / 4 = -28/4 and +14/4 = -7 and 7/2
Thus f'(x) = 0 at x=-7 and x=7/2
f'(x) <0 for the interval (-7,7/2) and f'(x) >0 for (-infinity , -7) U (7/2, infinity)

Thus f is increasing for (-infinity , -7) U (7/2 , infinity)
f is decreasing for (-7,7/2)

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.