Example 3:
Differentiate y = (x+2) (x+3) by using the formul..
Differentiate y = (x+2) (x+3) by using the formul..Note 3:
d y and dy are not usually the same and dy is the approximate value of d y..
d y and dy are not usually the same and dy is the approximate value of d y..Step 3:
Check the sign of f'(x) in the immediate neighbourhood of each critical valu..
Step 3:
Check if f (a) = f (b) If all the above condition are satisfied, then Rolle's theorem is applicable else the Rolle's theorem is not applicable. If Rolle's theorem is applicable, solve f '(c) = 0. Show that one of these roots lie in the open interval (a, b..
Note 3:
Equation of the tangent at (x 1 ,y 1 ) is or ..
Equation of the tangent at (x 1 ,y 1 ) is or ..Note 3:
Every polynomial function is continuou..
Theorem 3: (Second Derivative Test)
Let f be a differentiable function on an interval I and let a I. Let f "(a) be continuous at a. Then i) 'a' is a point of local maxima if f '(a) = 0 and f "(a) < 0 ii) 'a' is a point of local minima if f '(a) = 0 and f "(a) > 0 iii) The test fails if f '(a) = 0 and f "(a) = 0. In this case we..
Let f be a differentiable function on an interval I and let a I. Let f "(a) be continuous at a. Then i) 'a' is a point of local maxima if f '(a) = 0 and f "(a) < 0 ii) 'a' is a point of local minima if f '(a) = 0 and f "(a) > 0 iii) The test fails if f '(a) = 0 and f "(a) = 0. In this case we..Example 2:
Differentiate cos - 1 (2x+3) from first principle..
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