he tangent line at $$x=0 has been graphed, and its equation can be approximated by $$y=2.1x+3. Use the tangent to calculate the instantaneous rate of change at $$x=0.
Question
he tangent line at x=0 has been graphed, and its equation can be approximated by y=2.1x+3. Use the tangent to calculate the instantaneous rate of change at x=0.
Solution
Para calcular la tasa de cambio instantánea en usando la línea tangente, seguimos estos pasos:
-
Identificar la ecuación de la línea tangente: La ecuación dada es .
-
Entender la relación de la línea tangente con la derivada: La pendiente de la línea tangente en un punto específico es igual a la derivada de la función en ese punto. En este caso, la pendiente de la línea tangente es 2.1.
-
Determinar la tasa de cambio instantánea: La tasa de cambio instantánea en es igual a la pendiente de la línea tangente en ese punto.
Por lo tanto, la tasa de cambio instantánea en es .
Similar Questions
For the given curve: y = 5x – 2x3, when x increases at the rate of 2 units/sec, then how fast is the slope of curve changes when x = 3?
Calculate the instantaneous rate of change to the graph ofxexf x sin73)( at x = 0. Showyour work
Determine the average rate of change of the function over theintervalb) Copy the graph, and draw a tangent line at the point whereDetermine the slope of the tangent line to estimate theinstantaneous rate of change at this point.2. Estimate the instantaneous rate of change of the function inquestion 1 at by determining the slope of a secant line fromthe point where to the point where Compare youranswer with your answer for question 1, part b).3. Use graphing technology to estimate the instantaneous rate of changeof the function in question 1 atPRACTISING4. Estimate the instantaneous rate of change of at thepoint (2, 21).f (x) 5 xx 2 4x 5 2.x 5 2.01.x 5 2x 5 2x 5 2.2 # x # 7.In SummaryKey Ideas• The methods that were previously used to calculate the average rate of changeand estimate the instantaneous rate of change can be used for rationalfunctions.• You cannot determine the average and instantaneous rates of change of arational function at a point where the graph is discontinuous (that is, wherethere is a hole or a vertical asymptote).Need to Know• The average rate of change of a rational function, on the intervalfrom is Graphically, this is equivalent to the slopeof the secant line that passes through the points and on thegraph of• The instantaneous rate of change of a rational function, at canbe approximated using the difference quotient and a very smallvalue of h. Graphically, this is equivalent to estimating the slope of the tangentline that passes through the point on the graph of• The instantaneous rate of change at a vertical asymptote is undefined. Theinstantaneous rates of change at points that are approaching a verticalasymptote become very large positive or very large negative values. Theinstantaneous rate of change near a horizontal asymptote approaches zero.y 5 f(x).(a, f(a))f(a 1 h) 2 f(a)hx 5 ay 5 f(x),y 5 f(x).(x2, y2)(x1, y1)f(x2) 2 f(x1)x2 2 x1 .x1 # x # x2y 5 f(x),01010–10–10yxy = x + 2——–-x – 1NEL 303Chapter 55.6
Determine the slope of the tangent line to estimate theinstantaneous rate of change at this point.
The topic is the application of function derivatives. The first task: Find the equation of the tangent line to 𝑦=2𝑥2−𝑥+3 at 𝑥0=0.5 Give explanations and formulas and draw a graph if needed
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.