根据题意:The equation of the tangent line就是求此点的切线方程,先求过此点切线的斜率:求导得:y'=(1/3)(18 -2x)^(1/3-1)=(1/3)(18 -2x)^(-2/3)=1/[3³√(18 -2x)²]把x=5代入得:y'=1/[3³√(18 -10)²]=1/[3³√64]=1/[3·(4)]=1/12即切线斜率=1/12;y=...
Calculus I: Lesson 6: Finding the Equation of a Tangent LineDr. Karen Brucks
Equations of a Tangent Line: A tangent line merely touches a point on a curve, just like, say, the floor touches a point on the surface of a ball that is lying still on the floor. The equation of a tangent line can be found using the point-slope...
Tangent and Normal Line: The equation of a tangent line to a curve {eq}f\left( x \right) {/eq} at a point {eq}\left( {{x_0},{y_0}} \right) {/eq} is given as: {eq}y - {y_0} = f'\left( {{x_0}} \right)\left( {x - {x_...
Let the equation of the tangent line be y= -x +b. Substituting this into the equation of the circle: 2x^2- 2bx+b^2-4=0 . Since the line is tangent to the circle, we have △=(-2b)^2-4*2(b^2-4)=0 Solving for b: b =±2 2. So the equation of the tangent line is ...
The equation of a tangent line on the curve is: {eq}y = m (x - x_1) + y_1 {/eq} Answer and Explanation:1 Given: {eq}\displaystyle f(x) = - \frac{1}{x^2} \text{ at point on the curve is } \left (\frac{1}{2}, - 4\right ) {/eq} ...
1线性近似法local linearizationif f' exist,the local linerization of f(x) at a is f(a)+f'(a)(x-a)since the equation of the tangent line to y=f(x) at x=a is y-f(a)=f'(a)(x-a)we see that the y value on the tagent line is an approximation for the true value of...
Finding the Equation of a Tangent Line Find the equation of the line tangent to the graph of f(x)=1/xf(x)=1/x at x=2x=2. Show Solution Find the slope of the line tangent to the graph of f(x)=√xf(x)=x at x=4x=4. Show Solution Hint Use either (Figure) or (Figure)....
Find the equation of line tangent to the graph of f(x)=e+ln x at x=1? 答案 e是常数,f'(x)=1/x,所以切线在x=1点的斜率是1,在x=1点的函数值是e.So the equation of the tangent line of graph at x=1 is f(x)=x+e-1相关推荐 1Find the equation of line tangent to the grap...
Find {eq}\displaystyle f'(x) {/eq} and find the equation of the line tangent to the graph of {eq}\displaystyle f {/eq} at {eq}\displaystyle x=2 {/eq} . {eq}\displaystyle f(x) = (1+5x)(5-2x) {/eq} Equation of a Tangent Line: Determi...