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
