Posted by Steff on Wednesday, June 15, 2011 at 8:26am.
Please help.
f(t)=(4+√t)(4t^25)
This is what I have so far...
(4+√t)(8t)+(4t^25) (1/2t^1/2)
Am struggling to get this in factored form. Am working on a multiple choice take home test and nothing I am getting matches.

derivative calculus  Jai, Wednesday, June 15, 2011 at 8:40am
the derivative you got is correct.
by distributing, we can further simplify this into:
32t + 8t^(3/2) + 2t^(3/2)  (5/2)t^(1/2)
10t^(3/2) + 32t  (5/2)t^(1/2)
hope this helps~ :)

derivative calculus  Reiny, Wednesday, June 15, 2011 at 8:42am
sofar ok
why don't we expand this ... and simplify to get
32t + 10t^(3/2)  (5/2)t^(1/2)
= 32t + 10t√t  5/(2√t)
Since I don't know what your choices are, I don't know in which direction to go from here.
Here is a good trick to see if your answer is the same as theirs.
Pick any point on the original
e.g. let t = 1
f(1) = 5(45) = 5
so (1,5)
so sub in t = 1 into our derivative answer to get
32(1) + 10(1)(1)  5/(2(1)) = 39.5
Any of the choices not giving you 39.5 would be incorrect.

derivative calculus  Steff, Wednesday, June 15, 2011 at 8:50am
Here are my options
a) 10t^2+32t√t  5 / √t
b) 20t^264t√t  5 / 2√t
c) 20t^2+ 32t√t  5 / 2√t
d) 20t^2+64t√t  5 / 2√t
e) 10t^232t√t  5 / √t

Multiple choice options  Steff, Wednesday, June 15, 2011 at 9:11am
added

derivative calculus  Reiny, Wednesday, June 15, 2011 at 10:22am
If c) is written as
(20t^2 + 32t√t  5)/(2√t) it would be same as my answer.
The formed a common denominator
the way you typed it, only the 5 would be divided by 2√t

derivative calculus  Steff, Wednesday, June 15, 2011 at 10:31am
Thanks. I see my mistake now.
Answer This Question
Related Questions
 Calc 1  √1+t√1t/t lim > 0 The answer is one and I am not ...
 Math  Find an equation of the line that bisects the obtuse angles formed by the...
 8th grade algebra  Can you check my answers? 1. 3√20/√4 = 3√(...
 Algebra  1. Simplify the expression: 4√18+5√32 A.45√2 B.32&#...
 Algebra 2  Can someone help me with this radical expression please? The problem...
 Math(I Don't Get THIS!!)  15sqrt8x^16/5sqrt2x^4 *I totally need help with this ...
 Algebra  Simplify the expressions and solve the equations 1. 2√3  √...
 Math help Ms. Sue please  1. What is the simplified form of the expression? 7m^...
 Algebra  Check My Work  For Question 18 Simplify the Radical Expression...
 Math  find the value of k in simplest form for which the larger root of x^25x+...
More Related Questions