Findf′(x)and find the equation of the line tangent to the graph offatx=2. f(x)=(1+5x)(5−2x) Equation of a Tangent Line: Determining the equation of a tangent line to a function is one of the applications of a function's derivative. This is because...
Learn about the slope of a line on a graph. Discover the slope formula, understand the difference between steep and gradual slopes, and graph the tangent to a curve. Related to this Question Find the equation of the tangent line to x^2 - x y + 3 y^2 = 3 at the point...
single point that line is called the tangent line. Now, if we know that the touching point is(x1,y1)and the slope of the tangent line ismthen the equation of the tangent line is(y−y1)=m(x−x1). This form of the equation is done by th...
Suppose the slope of a perpendicular line is represented as {eq}m_1 {/eq} then substitute this value with the coordinates of the point {eq}(x_1, y_1) {/eq} in the general formula given below and simplify it for the perpendicular line. {eq}\displaystyle y-y_1...
Therefore, the slope of the tangent becomes (dy/dx)x = x1 ; y = y1. Now since we have found how to calculate the slope, we can simply go forward with following the concept of coordinate geometry according to which an equation of a line is (y − y1) = m(x − x1) , ...
The equation of a line is linear in two variables, usually x and y, that is satisfied by points of the line. The equation of line is usually found by the point-slope form y - y_1 = m (x - x_1), where m is the slope and (x_1, y_1) is a point on the line.
If a function is given by f(x)=e^( x/7), which of the following is an equation of the line tangent to the graph of f(x) when f(x)=e? ( ) A. y-e= 17e(x-7) B. y-e=-7e(x-7) C. y-7=-7e(x-e) D. y-7= 17e(x-e)...
Step 1: Find the derivatives dydθ and dxdθ 1. Differentiate y with respect to θ: y=1+cosθ⟹dydθ=−sinθ 2. Differentiate x with respect to θ: x=θ+sinθ⟹dxdθ=1+cosθ Step 2: Find the slope m of the tangent line Using the formula for the slope of the tangent line...
A curve in the plane is defined by the parametric equationsx=e2t+2e−1andy=e2t+et.An equation for the line tangent to the curve at the pointt=ln2is5x−6y=7(b)5x−3y=710x−7y=8(d)3x−2y=3 View Solution Find the differentiation ofe2x+e−2xe2x−e−2xw.r.t.x ...
Example 1. Find the equation of a line passing through two points A(1, 7) and B(2, 3). Solution. We use the formula for the equation of a straight line passing through two points x - 12 - 1 = y - 73 - 7 From this equation, we express y in terms of x x - 11 = y - ...