1) Which is the best method to use to find df/dt if
f(t)=(9x^2 + 3x - 14)^12 ?
Chain rule because this is a function of a function.
So you get 12*(expression)^ 11 multiplied by diff of (expression)
2)Which of the following mathematical terms was used in defining differential calculus?
We did not see the version of the definition that you did,
but the general idea is about "rate of change" as in:-
Differential calculus is the study of slopes of curves, accelerations, maxima, and minima by means of derivatives and differentials. It is the mathematics of the variation of a function with respect to changes in independent variables.
So given the 4 options
a) Y-intercept b) exponents c) polynomials d) linear slope, perhaps linear slope was
used as an introductory concept.
Best that you read your teacher's definition to check .
3) Which of the following will best solve this problem: h(x) = (14x-13)?
a) power rule b) product rule c) quotient rule d) all of the above would work well
Those question marks are back again.
Please fix this by using a different font or symbol and
reading your postings before submitting.
I am forced to guess it was someting like h(x) = (14x-13)^12
in which case it is like 1) so the power rule is the main one,
but do not forget to multiply by diff of (expression).
On the other hand if the ? meant something else, such as another expression it might be the product rule. So reread your original question.
4)You wrote: Which of the following is w(x) if w' (x)= 3x^2 =6x?
a) 3x^2 + 6x
b) 6x+6
c)3x^3 = 3x^2
d) x^3 + 3x^2
Now we seem to have a random sprinkling of = signs instead of + signs with another question mark floating about.
I think the question should have read:
Which of the following is w(x) if w' (x) = 3x^2 + 6x
a) 3x^2 + 6x
b) 6x+6
c)3x^3 + 3x^2
d) x^3 + 3x^2
The answer is d), because, using the power rule
d/dx[x^3 + 3x^2] = 3x^2 + 6x
?
5) Which of the following starting values of x_n would likely converge quickest to finding the square root of 19 using the Babylonian Method?
a) 4.3
b) 4
c) 17
d) -6
The Babylonian Method involves dividing and averaging, over and over, to find a more accurate estimate of the square root with each repeat of the process.
The square root of 19 is about 4.3588 so the start value nearest to this is likely converge quickest, and this value is a) 4.3
I am trying to be of help, but much of this is a guessing game due to the way you posted.
Regards - Ian
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