Question 1152830: If dy/dx is 6x^2+4x-5, and y=10 when x=2, find the value of y when x=3. please with full working
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source):
Answer by ikleyn(52780)  (Show Source):
You can put this solution on YOUR website! .
It is very standard Calculus problem, typical for beginner Calculus students,
and the solution by @MathLover1 is A B S O L U T E L Y W R O N G.
Below find the correct solution, instead.
Consider ANTIderivative, which is the general solution to the given differential equation
y = 2x^3 + 2x^2 - 5x + C, (1)
where C is an arbitrary constant.
We define the value of this constant from the given condition y= 10 at x= 2.
Substitute x= 2 into (1) to get
10 = 2^2^3 + 2*2^2 - 5x + c,
10 = 2*8 + 2*4 - 5*2 + C = 16 + 8 - 10 + C = C + 14,
which implies
C = 10 - 14 = -4.
So, the specific solution to the given differential equation under the given condition at the point x= 2 is
y = 2x^3 + 2x^2 - 5x - 4. (2)
Now the value of y at x= 3 is
y = 2*3^3 + 2*3^2 - 5*3 - 4 = 53. ANSWER
Solved, answered, explained (in all details) and completed.
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Having this text before your eyes, printed or in the screen of your computer,
you may boldly go to a Calculus class and to give a PRESENTATION (a lecture)
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You may use this post for many other similar problems, with the equal success.
(It is partly a joke, of course, but partly is TRUTH, in great part . . . )
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