Part A. You have the correct first and second derivative.
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Part B. You'll need to be more specific. What I would do is show how the quantity (-2x+1)^4 is always nonnegative. This is because x^4 = (x^2)^2 is always nonnegative. So (-2x+1)^4 >= 0. The coefficient -10a is either positive or negative depending on the value of 'a'. If a > 0, then -10a is negative. Making h ' (x) negative. So in this case, h(x) is monotonically decreasing always. On the flip side, if a < 0, then h ' (x) is monotonically increasing as h ' (x) is positive.
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Part C. What this is saying is basically "if we change 'a' and/or 'b', then the extrema will NOT change". So is that the case? Let's find out
To find the relative extrema, aka local extrema, we plug in h ' (x) = 0
h ' (x) = -10a(-2x+1)^4
0 = -10a(-2x+1)^4
so either
-10a = 0 or (-2x+1)^4 = 0
The first part is all we care about. Solving for 'a' gets us a = 0.
But there's a problem. It's clearly stated that 'a' is nonzero. So in any other case, the value of 'a' doesn't lead to altering the path in terms of finding the extrema. We'll focus on solving (-2x+1)^4 = 0 for x. Also, the parameter b is nowhere to be found in h ' (x) so that's out as well.
Answer:
I cant lie I don't know this answer
Answer:
3.002 * 10⁵
Step-by-step explanation:
3 * 10⁵ = 3 * 10³ * 10² = 3000 *10²
3 * 10⁵ + 2* 10² = 3000 * 10² + 2*10²
= (3000 + 2) * 10²
= 3002 * 10²
= 3.002 * 10³ * 10²
= 3.002 * 10⁵

Substitute the given value of x into the first equation

To solve for x distribute 3 though the parentheses

Collect like terms

Move the constant to the right-hand side and change its sign

Add the numbers

Divide both sides of the equation by 13

Now, Substitute the given value of x into the second equation

Plug in the value of x in the equation i.e. 1

Any number multiplied by 1 results in number itself

Calculate the difference

The possible solution of the system is the ordered pair (x,y)

Answer:
9p+3r−7
Step-by-step explanation:
=3r+12p+−7+−3p
Combine Like Terms:
=3r+12p+−7+−3p
=(12p+−3p)+(3r)+(−7)
=9p+3r+−7