一定注意SD:f″(x)=0 or DNE,然后判断是否是concave up和concave down 的转折点,才能确定是否 point of inflection。 一定注意variable upper bound function: g(x)=∫axf(t)dt, g′(x)=f(x),如果h(x)=∫ak(x)f(t)dt,则h′(x)=f(k(x))k′(x),即chain rule. 对于position vector(x(t),...
3.求f’’(x)→找concave up和concave down还有拐点inflection point 7.Mean value Theorem应用( P190-43.44 ) 8.求方程根的近似解 1.二分法Bisection Method 2.牛顿法Newton’s Method = – 3.Fixed-PointAlgotithm = g( ) 9.Antiderivative→Integral 处理Differential Equations 1. =ky→ (可由一阶线性...
State the intervals where g(x) is concave up and concave down. c. Graph the function by hand using the above points and any intercepts that you can find. f(x)=6(4-3x4)2 a. Find all the critical points and use the First Deriva...
(b) Is the graph of f concave up or concave down on the interval 1 < x < 3 ? Give a reason for your answer. (c) Use antidifferentiation to find f ( x ) . t (minutes) r ? (t ) (feet per minute) 0 5.7 2 4.0 5 2.0 7 1.2 11 0.6 12 0.5 5. The volume of a spherical...
relative --> find critical points, make f' line, plug into f'(x) 1st derivative test 1. left/right2. max/min3. increasing/ decreasing 2nd derivative test 1. speeding up/slowing down2. points of inflection3. concave up/concave down...
In both cases the function is increasing and the first derivative is always positive; however each function increases in a different way i.e. one increases concave up and the other increases concave down. Using the first derivative only, we would have to know not only where its positive or ...
WARNING: Don't abandon your precalculus skills, and common sense! f'>0 \rightarrow f is increasing. f'<0 \rightarrow f is decreasing. f''>0 \rightarrow f' is increasing, f is concave up. f''<0 \rightarrow f' is decreasing, f is concave down. ...
Is the graph of y f =()x concave up or concave down at the dx point (1, 3) ? Give a reason for your answer. D . r e o n d r o o t b w s r i h i t t e b d e n y o o y n e d b e t t i h i r s w b t o o r d n o e r . D GO ON TO...
Concave Up and Down Constant Term Continued Sum Conditional Convergence Convergence of Random Variables Critical Numbers Curly d Curvilinear Cylindrical Coordinates D Del Operator (Nabla operator) Definite Integral Deleted Neighborhood Difference Quotient Differentiable Differential Approximation Differential Operator...
Our textbook (along with the world of math) has adopted the rule of four. Just like Pre Calculus we will be exploring Calculus graphically, numerically, algebraically, and verbally. We will find the connections between graphs (with out equations) and data and how it relates to a graph. ...