The polynomial functions that has the largest second derivative at x = 0 is; y = x³ + 2x² - 5x + 10
<h3>How to find the second derivative of a Polynomial?</h3>
The second derivative of a function is simply defined as the derivative of the function's derivative.
Thus;
A) If y = 5x⁵ - x³ + 4x
dy/dx = 25x⁴ - 3x² + 4
d²y/dx² = 100x³ - 6x
Thus at x = 0, we have;
d²y/dx² = 0
B) y = 3x⁴ + x² + 16
dy/dx = 12x³ + 2x
d²y/dx² = 36x² + 2
At x = 0, the second derivative is;
d²y/dx² = 2
C) y = 4x⁶ + x² - 1
dy/dx = 24x⁵ + 2x - 1
d²y/dx² = 48x⁴ + 2
At x = 0, the second derivative is;
d²y/dx² = 2
D) y = x³ + 2x² - 5x + 10
dy/dx = 3x² + 4x - 5
d²y/dx² = 6x + 4
At x = 0, the second derivative is;
d²y/dx² = 4
E) y = 10x⁵ + 3x³ - 7x + 2
dy/dx = 50x⁴ + 9x² - 7
d²y/dx² = 200x³ + 18x
At x = 0, the second derivative is;
d²y/dx² = 0
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Answer:
Step-by-step explanation:
To find the inverse of a function, switch the x and y values and isolate y. After switching the x and y values of 
, we get 
.
Now divide by 2 to isolate y:
Answer:
A- You will be charged interest on your remaining balance.
C- You may be in debt for a long time.
Step-by-step explanation:
The following are true if you pay only the minimum amount each month towards your credit card bill:
Firstly one will be charged interest on the remaining amount. Suppose you had a bill of $500. But you paid the minimum of $100. So, you will be charged your standard interest rate on $400.
And with this format, one will be in a debt for a long time as each month some new balance will be added to the previous one.
So, options A and C are true.
B is not true as the interest rates are not changed during the cycle.
Answer:
- (x + 3)(x - 3)(x^2 -3x + 9)(x^2 + 3x + 9)
Step-by-step explanation:
<u><em>Use of formulas:</em></u>
- <em>a^2 - b^2 = (a + b)(a -b)</em>
- <em>a^3 + b^3 = (a + b)(a^2 - ab + b^2)</em>
- <em>a^3 - b^3 = (a - b)(a^2 + ab + b^2)</em>
<u>Given the expression: </u>
<u>Factoring 729</u>
<u>Factoring the expression </u>
- x^6 - 3^6 =
- (x^3)^2 - (3^3)^2 =
- (x^3 + 3^3)(x^3 - 3^3) =
- (x + 3)(x^2 -3x + 9)(x - 3)(x^2 + 3x + 9) =
- (x + 3)(x - 3)(x^2 -3x + 9)(x^2 + 3x + 9)
