What is the minimum slope of y=x^3-9x^2+15x? matlab code

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Busra Tabak 2018-12-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/435989-what-is-the-minimum-slope-of-y-x-3-9-x-2-15-x-matlab-code

评论： Image Analyst 2018-12-16

What is the minimum slope of y=x^3-9*x^2+15*x?

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madhan ravi 2018-12-16

what have you tried so far?

Busra Tabak 2018-12-16

在 MATLAB Online 中打开

syms x
f=x^3-9*x^2+15*x;
fprime=diff(f,x);
fdprime=diff(fprime,x);
xstar=double(solve(fprime==0,x));
xstar=unique(xstar);
for i=1:numel(xstar)
    if subs(fdprime,x,xstar(i))>0
        disp('min')
    double(subs(f,x,xstar(i)))
    end
end
 

I wrote this code and got this solution. Is it correct?

min
 
ans =
 
   -25

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Answer 1

Image Analyst 2018-12-16

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https://ww2.mathworks.cn/matlabcentral/answers/435989-what-is-the-minimum-slope-of-y-x-3-9-x-2-15-x-matlab-code#answer_352646

在 MATLAB Online 中打开

Hint:

slope = 3 * x .^ 2 - 18 * x + 15; % Derivative.
minSlope = min(slope)
minAbsSlope = min(abs(slope))

Plot it, using linspace() for x, and see what you see. Of course since it's a parabola, the min absolute value of the slope will be zero and the min slope will depend on how far negative you want to evaluate x. For x that is more negative, the slope will be steeper.

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Busra Tabak 2018-12-16

I do not understand and I can not write the code. Did you find -25 as answer?

Image Analyst 2018-12-16

在 MATLAB Online 中打开

No, of course not. Did you just plot the function and see it? Nowhere does it turn downwards and have a negative slope:

x = linspace(-50, 50, 100000);
y = x.^3-9*x.^2+15*x;
subplot(2, 1, 1);
plot(x, y, 'b-')
grid on;
fontSize = 20;
title('y = x .^ 3 - 9 * x .^ 2 + 15 * x', 'FontSize', fontSize, 'Interpreter', 'none');
xlabel('x', 'FontSize', fontSize, 'Interpreter', 'none');
ylabel('y', 'FontSize', fontSize, 'Interpreter', 'none');
slope = 3 * x .^ 2 - 18 * x + 15; % Derivative.
minSlope = min(slope)
minAbsSlope = min(abs(slope))
subplot(2, 1, 2);
plot(x, slope, 'b-')
xlabel('x', 'FontSize', fontSize, 'Interpreter', 'none');
ylabel('Slope of y', 'FontSize', fontSize, 'Interpreter', 'none');
title('slope = 3 * x .^ 2 - 18 * x + 15', 'FontSize', fontSize, 'Interpreter', 'none');
grid on;

It's a parabola so what do you think the min absolute slope would be? And don't you see and understand that the min slope (most negative) will depend on how far out into the negative x territory you want to go?

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