Maths differentiation
2007-12-01 07:46:18 · 6 answers · asked by ja 2 in Science & Mathematics ➔ Mathematics
Let f(x) = x³ + x² + 5x + 3.
Gradient of the curve at any point =
derivative of the curve at any point.
So f'(x) = 3x² + 2x + 5
and we have to solve
3x² + 2x + 5 = 0.
But the discriminant of this quadratic is
4 - 60 = -56 < 0,
so this equation has no real roots.
Thus the gradient of the curve is never 0.
2007-12-01 08:21:40 · answer #1 · answered by steiner1745 7 · 0⤊ 1⤋
in case you ever took precalculus or another math classification which covers houses of applications, you the right thanks to envision the area of the function. between the pink flags to look out for is once you divide by ability of 0. on your expression, even as x = 3, the denominator is 0. hence, the area is each huge style beside 3. regrettably, the large style you're attempting to plug in (x = 3) is the in basic terms huge style that would not paintings in this function. to work out this wide-spread hand, you0 can graph this function on a TI-80 3. in case you zoom in on the point of the graph at x = 3, you'll discover there's a sparkling spot there! this is because, as suggested above, there basically isn't a fee of the expression at x = 3. you would possibly want to assert, nicely it sounds like the answer should be 6, depending on the graph. this idea of what the answer "should be" is what limits are all about. The values of the function on the left and properly of x = 3 all bypass in the route of 6 as you seize up with and closer. So we are saying the decrease as x is going to three is 6. So regardless of the particular undeniable actuality that it's not technically the answer, 6 is your fantastic decision. 0 isn't best in any experience. the very fantastic answer is to assert that the expression is undefined at x = 3. This difficulty illustrates why 0/0 is termed indeterminate. in this difficulty, 0/0 in a way equals 6. the concept 0/0 can equivalent some thing is genuinely the essence of calculus.
2016-10-25 06:36:20 · answer #2 · answered by fireman 4 · 0⤊ 0⤋
The question is nonsense, the function prodcues a "tan" like result... perhaps at +0 and -0 will surfice as an answer.
2007-12-01 08:07:16 · answer #3 · answered by Paine 6 · 0⤊ 1⤋
i cant coz i iz fick
2007-12-01 07:49:04 · answer #4 · answered by Scott S 4 · 0⤊ 1⤋
do your own work LAZY
2007-12-01 07:48:46 · answer #5 · answered by Anonymous · 0⤊ 1⤋
Why?
2007-12-01 07:48:48 · answer #6 · answered by Anonymous · 0⤊ 1⤋