second derivative and applications of calculus (1 Viewer)

[apak]

second derivative and applications of calculus (solved)

I have previously done these question but now im not sure how to doo it........
question : By considering the sign of f'x and f''x sketch the shape oft he cure y=f(x) in the give domains
a)y=x^3 from x=1 to x=3

the answer is the 2 points and a curved line joining them. you can get the answer by puttin x values in for y. But what are they asking for?
are we ment to test 1 and 3 in the first derivative to see which one's gradient is greator thus which slops more or do we check the concavity at those points. i cant remember what did last time but im pretty sure its one of them.
Its the 3 u book page 22
thx in adv

 

[pLuvia]

It just means by considering the first derivative (the stationary points, and the point of inflextions) and the second derivative (the nature of them) draw the curve y=f(x)

I think

 

[insert-username]

Whenever a question asks "by considering the sign of f'x and f''x...", you must find the first and second derivatives of the function. You cannot substitute in points as that is not what the question is asking. The first derivative tells you the sign of the gradient and any stationary points. The second derivative tells you whether the curve is concave up (f''(x) positive), concave down (f''(x) negative), or a point of inflexion (f''(x) = 0).


I_F

 

[apak]

yea i know what both of you are saying but
"It just means by considering the first derivative (the stationary points, and the point of inflextions) and the second derivative (the nature of them) draw the curve y=f(x)"
they are not asking you to find that.. they have the 2 points and they want you see if it goes concave up or downwards. To find the answer u gotta sub the 2 points into the first derivative and second derivative.
Wait i remember !!!!!!! the 2nd derivative will show u if its concave up or down then the first derivative will show u if the gradient is pos or neg so you'll know how it looks like!! i remember
thx guys

 

[pLuvia]

yea i know what both of you are saying but
"It just means by considering the first derivative (the stationary points, and the point of inflextions) and the second derivative (the nature of them) draw the curve y=f(x)"
they are not asking you to find that.. they have the 2 points and they want you see if it goes concave up or downwards. To find the answer u gotta sub the 2 points into the first derivative and second derivative.
Wait i remember !!!!!!! the 2nd derivative will show u if its concave up or down then the first derivative will show u if the gradient is pos or neg so you'll know how it looks like!! i remember
thx guys

lol .

 

[Riviet]

Another way of explaining the purpose of the 1st deriv. is determining whether the curve is decreasing or increasing at a point, ie the gradient.